Classical Dynamical Entropy
Classical Dynamical Entropy
This chapter applies the algebraic formalism to classical dynamical systems, in particular, the notion of dynamical entropy developed in the previous chapter in terms of operational partitions is equivalent to the standard Kolmogorov–Sinai invariant. A characterization of partitions that are sufficiently fine to reach the KS-invariant is given in terms of H-dense sub-algebras, and then is applied to unimodular orthonormal systems. The new formalism provides new techniques for computing the KS-entropy that is illustrated by the examples of expanding maps and Arnold cat maps.
Keywords: KS-entropy, H-dense sub-algebra, unimodular orthonormal systems, KS-invariant, Arnold cat maps
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